Automated computer evaluation and optimization of image compression of x-ray coronary angiograms for signal known exactly detection tasks

Miguel P. Eckstein; Jay L. Bartroff; Craig K. Abbey; James S. Whiting; Francois O. Bochud

doi:10.1364/OE.11.000460

Optics Express
Vol. 11,
Issue 5,
pp. 460-475
(2003)
•https://doi.org/10.1364/OE.11.000460

Automated computer evaluation and optimization of image compression of x-ray coronary angiograms for signal known exactly detection tasks

Miguel P. Eckstein, Jay L. Bartroff, Craig K. Abbey, James S. Whiting, and Francois O. Bochud

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Miguel P. Eckstein, Jay L. Bartroff, Craig K. Abbey, James S. Whiting, and Francois O. Bochud, "Automated computer evaluation and optimization of image compression of x-ray coronary angiograms for signal known exactly detection tasks," Opt. Express 11, 460-475 (2003)

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Abstract

We compared the ability of three model observers (nonprewhitening matched filter with an eye filter, Hotelling and channelized Hotelling) in predicting the effect of JPEG and wavelet-Crewcode image compression on human visual detection of a simulated lesion in single frame digital x-ray coronary angiograms. All three model observers predicted the JPEG superiority present in human performance, although the nonprewhitening matched filter with an eye filter (NPWE) and the channelized Hotelling models were better predictors than the Hotelling model. The commonly used root mean square error and related peak signal to noise ratio metrics incorrectly predicted a JPEG inferiority. A particular image discrimination/perceptual difference model correctly predicted a JPEG advantage at low compression ratios but incorrectly predicted a JPEG inferiority at high compression ratios. In the second part of the paper, the NPWE model was used to perform automated simulated annealing optimization of the quantization matrix of the JPEG algorithm at 25:1 compression ratio. A subsequent psychophysical study resulted in improved human detection performance for images compressed with the NPWE optimized quantization matrix over the JPEG default quantization matrix. Together, our results show how model observers can be successfully used to perform automated evaluation and optimization of diagnostic performance in clinically relevant visual tasks using real anatomic backgrounds.

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Fig. 1. Human (red squares for JPEG, blue triangles for wavelet Crewcode) vs. model performance (empty squares and continuous line). Different rows are for different model observes (NPWE; Non-Prewhitening matched filter with an eye filter, CH-Hot: channelized Hotelling; HOT: Hotelling) as a function of compression ratio. Top line is for JPEG and bottom line is for wavelet Crewcode. Left and right columns non-physician observers: GR and CH.

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Fig. 2. Physician (red symbols, JPEG; blue symbols wavelet-Crewcode) vs. model observer performance. Different panels are for different model observers as a function of compression ratio.

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Fig. 3. Left: Root mean square error between original and image undergoing different degrees of compression (averaged across the 424 test images) for the JPEG (red squares) and wavelet-Crewcode algorithms (blue triangles). Right: DC-tune 2.0 metric as a function of image compression for the JPEG and wavelet-Crewcode algorithms.

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Fig. 4: Simulated Annealing procedure applied to the optimization of the JPEG quantization matrix based on model observer performance following Smith (1985)

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Fig. 5. Top left: Performance of the NPWE model for three different quantization matrices. Top right: Performance for NPWE model across compression ratios for the default quantization matrix and the 25:1 optimized quantization matrix. Bottom left: Performance for observer GR for three quantization matrices. Bottom right: Performance for physician observer DV for three quantization matrices

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Tables (2)

Table 1. Goodness of fit assessed with a reduced Chi-square ( ${χ_{r}}^{2}$ ), for the three models to individual data for JPEG, Crewcode-wavelet and pooled across both algorithms and observers. Highlighted numbers correspond to lowest reduced chi-square value within a condition. Reduced Chi-squared is defined as $χ_{r}^{2} = \frac{1}{n - p} \sum_{i = 0}^{n} \frac{{(d_{h, i}^{'} - d_{m, i}^{'})}^{2}}{σ_{i}^{2}}$ , where d’_h,i is for the human in the i^th condition, d’_m,i is for the model, $σ_{i}^{2}$ is the observed variance of the human d’_h,i, n is the number of data points (n=10) and p is the number of fitting parameters (p=1).

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Table 2. Quantization matrix for the default JPEG standard

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Equations (14)

Equations on this page are rendered with MathJax. Learn more.

λ_{m} = \sum_{x = 1}^{N} \sum_{y = 1}^{N} w (x, y) g_{m} (x, y)

λ_{m} = w^{t} g_{m}

w (x, y) = {FFT}^{- 1} [s (u, v) {∣ E (u, v) ∣}^{2}]

E (f) = f^{ρ} \exp (- {cf}^{γ})

w_{h} = K^{- 1} [< g_{s} > - < g_{b} >]

V (x, y) = \exp [\frac{- 4 \ln 2 (x^{2} + y^{2})}{W_{s}^{2}}] \cos [2 π f_{c} (x \cos θ + y \sin θ) + β]

b w = \log_{2} [\frac{f_{c} + \frac{1}{2} W_{f}}{f_{c} - \frac{1}{2} W_{f}}]

a = K_{V}^{- 1} [< g_{\frac{V}{s}} > - < g_{\frac{V}{b}} >]

w (x, y) = \sum_{i = 0}^{N} a_{i} \cdot V_{i} (x, y)

λ_{m} = λ_{m, e} + ε_{m}

\hat{P} c = \frac{1}{J} \sum_{j = 1}^{J} step (λ_{s, j} - max_{i} (λ_{b, ij}))

Pc (d_{mafc}, M) = \int_{- \infty}^{+ \infty} φ (z - d_{mafc}) {[ϕ (z)]}^{M - 1} dz

RMSE = \sqrt{\frac{1}{XY} \sum_{x = 0}^{X} \sum_{y = 0}^{Y} {[I (x, y) - I_{c} (x, y)]}^{2}}

{c'}_{i, j} = round (\frac{c_{i, j}}{q_{i, j}})

Model	GR-JPEG	CH-JPEG	JH-JPEG	ALL-JPEG
NPWE	3.58	4.46	2.01	3.43
Channelized Hotelling (CH-HOT)	2.08	3.166	4.40	3.15
Hotelling (HOT)	17.81	13.67	17.41	16.23

16	11	10	16	24	40	51	61
12	12	14	19	26	58	60	55
14	13	16	24	40	57	69	56
14	17	22	29	51	87	80	62
18	22	37	56	68	109	103	77
24	35	55	64	81	104	113	92
49	64	78	87	103	121	120	101
72	92	95	98	112	100	103	99

Model	GR-JPEG	CH-JPEG	JH-JPEG	ALL-JPEG
NPWE	3.58	4.46	2.01	3.43
Channelized Hotelling (CH-HOT)	2.08	3.166	4.40	3.15
Hotelling (HOT)	17.81	13.67	17.41	16.23

16	11	10	16	24	40	51	61
12	12	14	19	26	58	60	55
14	13	16	24	40	57	69	56
14	17	22	29	51	87	80	62
18	22	37	56	68	109	103	77
24	35	55	64	81	104	113	92
49	64	78	87	103	121	120	101
72	92	95	98	112	100	103	99

16	11	10	16	24	40	51	61
12	12	14	19	26	58	60	55
14	13	16	24	40	57	69	56
14	17	22	29	51	87	80	62
18	22	37	56	68	109	103	77
24	35	55	64	81	104	113	92
49	64	78	87	103	121	120	101
72	92	95	98	112	100	103	99

16	11	10	16	24	40	51	61
12	12	14	19	26	58	60	55
14	13	16	24	40	57	69	56
14	17	22	29	51	87	80	62
18	22	37	56	68	109	103	77
24	35	55	64	81	104	113	92
49	64	78	87	103	121	120	101
72	92	95	98	112	100	103	99

16	11	10	16	24	40	51	61
12	12	14	19	26	58	60	55
14	13	16	24	40	57	69	56
14	17	22	29	51	87	80	62
18	22	37	56	68	109	103	77
24	35	55	64	81	104	113	92
49	64	78	87	103	121	120	101
72	92	95	98	112	100	103	99

16	11	10	16	24	40	51	61
12	12	14	19	26	58	60	55
14	13	16	24	40	57	69	56
14	17	22	29	51	87	80	62
18	22	37	56	68	109	103	77
24	35	55	64	81	104	113	92
49	64	78	87	103	121	120	101
72	92	95	98	112	100	103	99

Abstract

Cited By

Figures (5)

Tables (2)

Equations (14)

Optics Express

16	11	10	16	24	40	51	61
12	12	14	19	26	58	60	55
14	13	16	24	40	57	69	56
14	17	22	29	51	87	80	62
18	22	37	56	68	109	103	77
24	35	55	64	81	104	113	92
49	64	78	87	103	121	120	101
72	92	95	98	112	100	103	99

16	11	10	16	24	40	51	61
12	12	14	19	26	58	60	55
14	13	16	24	40	57	69	56
14	17	22	29	51	87	80	62
18	22	37	56	68	109	103	77
24	35	55	64	81	104	113	92
49	64	78	87	103	121	120	101
72	92	95	98	112	100	103	99